factor-5h^4-15h^3-10h^2

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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inflection points f(x)=sin(x)

Solution

(2πn, 0), (π+2πn, 0)

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Inflection points definition

An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
If f ′′(x)>0 then f(x) concave upwards.
If f ′′(x)<0 then f(x) concave downwards.

Find where f ′′(x) is equal to zero or undefined

x=2πn, x=π+2πn

Identify inflection points not in domain or where f(x) is not continuous

Domain of sin(x) : −∞ <x<∞

All inflection points are in domain and not on domain edges

x=2πn, x=π+2πn

Find intervals: Concave Downward:2πn<x<π+2πn, Concave Upward:π+2πn<x<2π+2πn

Plug x=2πn into sin(x): 0

(2πn, 0)

Plug x=π+2πn into sin(x): 0

(π+2πn, 0)

(2πn, 0), (π+2πn, 0)

Solve instead

domain sin(x)

range sin(x)

periodicity sin(x)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

factor-5h^4-15h^3-10h^2

Solution

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